Geodesic
Free Algebras of Automorphic Forms on the Upper Half-Plane
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 81-89.

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We find all pairs $(\Gamma,a)$ consisting of a cocompact Fuchsian group $\Gamma$ of genus zero and an automorphy factor $a$ of $\Gamma$ for which the graded algebra of $a$-$\Gamma$-automorphic forms is free.
Keywords: Fuchsian group, cocycle, automorphic form, free algebra. 
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O. V. Schwarzman. Free Algebras of Automorphic Forms on the Upper Half-Plane. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 81-89. http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a8/

[1] Gashkov S. B., Chubarikov V. N., Arifmetika, algoritmy, slozhnost vychislenii, Vysshaya shkola, M., 2000

[2] Dolgachev I. V., “Avtomorfnye formy i kvaziodnorodnye osobennosti”, Funkts. analiz i ego pril., 9:2 (1975), 67–68 | MR | Zbl

[3] Kra I., Avtomorfnye formy i kleinovy gruppy, Mir, M., 1975 | MR | Zbl

[4] Shvartsman O. V., “Svobodnye G-puchki na zamknutykh rimanovykh poverkhnostyakh”, UMN, 54:6 (1999), 175–176 | DOI | MR | Zbl

[5] Shvartsman O. V., “O kotsiklakh grupp kompleksnykh otrazhenii i silnoi odnosvyaznosti faktorprostranstv”, Voprosy teorii grupp i gomologicheskoi algebry, 1991, 32–39 | MR | Zbl

[6] Shimura G., Vvedenie v arifmeticheskuyu teoriyu avtomorfnykh funktsii, Mir, M., 1973 | MR | Zbl

[7] Tsishang Kh., Fogt E., Koldevai Kh.-D., Poverkhnosti i razryvnye gruppy, Nauka, M., 1988 | MR

[8] Baily W., Introductory lectures on automorphic forms, Princeton Univ. Press, 1973 | MR | Zbl

[9] Dolgachev I. V., “Invariant stable bundles over modular curves $X(p)$”, Contemp. Math., 224 (1999), 65–69 | DOI | MR

[10] Futura M., Steer B., “Seifert fibered homology $3$-spheres and the Yang–Mills equations on Riemann surfaces with marked points”, Adv. Math., 96 (1992), 38–102 | DOI | MR

[11] Kawasaki T., “The Riemann–Roch theorem for complex V-manifolds”, Osaka J. Math., 16 (1979), 151–159 | MR | Zbl

[12] Shephard G., Todd J., “Finite unitary reflection groups”, Canad. J. Math., 25 (1954), 159–198 | MR

[13] Wagreich P., “Algebras of automorphic forms with few generators”, Trans. Amer. Math. Soc., 262 (1980), 367–389 | DOI | MR | Zbl